Teachin g N o tes
Operation a l Reacto r Saf et y Course
Lecture : 3 – Reacto r Kin e tic s an d Control
Objectiv e:
To introduce the concept of prom pt and de layed neutrons and poi nt kinetics equations, reactivity, and the Inhour equation. Feedb ack effects are discu ssed including Doppler, moderator, void, fuel, etc. This is followed by a brief discussion of reactor control and power.
Ke y Point s t o Brin g Out:
Slid e num ber Point s
3 Here we want to introduce the key concepts of the tim e dependent diffusion equation and the definition of reactivity. Mean generation tim e is an important co ncept s i nce it iden tifies the speed with which thing s occur with out delay e d neutrons. Discuss the concept of a reacto r period being the cha nge in reactivity divided by the m ean generation tim e .
4 The im portance of delayed neut rons should be emphasized as being a s i gnificant aspect of reactor c ontrol.
5 Identifies th e typical s i x precu rsors of delayed neutrons as precursor groups with a total de layed neutron fraction of .0065. which allow s therm al re actors to be contro lled.
6 Identifies the various neutrons com i ng from time dependent neutron balance equations.
7 Presents the point kinetics and I nhour equations to the students as shown in the attached class notes . W r ite them on the board from Kneif.
8 The key point is to identify th e im portance of delayed neutrons. Noting the difference in delayed neutron fraction of Pu vs U235 and the energy at which delayed neutrons are born.
9 Key points here are to point out how reactors behave in response to a change in reactivity, either posit ive or negative. The im pact of the prom pt neutron population follow e d by an asymptotic effect of delayed neu t rons. Key factor for th erm al reactors is tha t the p eriod of the core is roughly 80 seconds to allow for m e asured start up.
10 These slides show the students the effect of prompt jum p and prom pt drops in term s of reactivity insertions.
11 Explain the various feedbacks th at o ccur and ho w they affect reactivity and why.
12 Coefficients are defined and de scribed. (Use Kneif definitions.)
13 Discusses the Doppler broade ning phenom enon. The key point is it’s an im portant con t ro l m echanis m for reacto r s. Doppler pro v ides a net in creas e in cros s section fo r rea ctor con t ro l for fast neutron trans i ents.
14 This slide pu ts the entir e reac tiv ity f eedback loo p into pe rsp ectiv e. Once there is a reactiv ity change whether it be the m ove m e nt of a control rod, the kinetic respons e is quite fast depending upon neutron lifetim e, which creates a local increas e in power, which can then be com p ensated for by fuel tem p erature, m oderator and density differences which m a y pr ovide negative feedbacks each with its own tim e constant ba sed on how quickly the phenomenon occur. The feedback loop determ ines whether reactor power goes up or down.
15 What happens in the h elium reactor for a drop in coolant tem p erature. It ends up being a pos itive reac tiv ity effect. The key point here is that the decrease in tem p eratu r e can increase po wer but ultim a tely be stabilized by other f eedback effects.
16 The key point here is to m a ke not e of the fact that the so luble boron m ay add positiv e reactivity as the tem p erature inc r eas e s. The moderator temperature coeffici ent is a function of the boron concentratio n which changes as a function of cycle life.
Also to be n oted are attached highlights of the Kneif text to allow one to develop the appropriate equations in the class lecture. Equations should be written in class to show the effect of prom pt and delayed ne utrons, the tim e dependant equations for the delayed groups, tim e dependant neutron ba lance equations for six delayed neutron groups as w e ll as the developm ent of the point kinetic equations. The highlighted sections are those th at sh oul d be brought out in class as part o f the lectu r e.
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22.091 / 22.903 Nuclear Reactor Safety
Spring 200 8
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